Univalency of Convolutions of Univalent Harmonic Right Half-Plane Mappings

Authors

Zhi Hong Liu, Hunan University
Saminathan Ponnusamy, Indian Statistical Institute Chennai

Article Type

Research Article

Publication Title

Computational Methods and Function Theory

Abstract

We consider the convolution of half-plane harmonic mappings with respective dilatations (z+ a) / (1 + az) and eiθzn, where - 1 < a< 1 and θ∈ R, n∈ N. We prove that such convolutions are locally univalent for n= 1 , which solves an open problem of Dorff et al. (see J Anal 18:69–81 [3, Problem 3.26]). Moreover, we provide some numerical computations to illustrate that such convolutions are not univalent for n≥ 2.

First Page

289

Last Page

302

DOI

10.1007/s40315-016-0180-0

Publication Date

6-1-2017

Comments

Open Access, Green

Recommended Citation

Liu, Zhi Hong and Ponnusamy, Saminathan, "Univalency of Convolutions of Univalent Harmonic Right Half-Plane Mappings" (2017). Journal Articles. 2544.
https://digitalcommons.isical.ac.in/journal-articles/2544